An improved adaptive response surface method for structural reliability analysis

The response surface method (RSM) is one of the main approaches for analyzing reliability problems with implicit performance functions. An improved adaptive RSM based on uniform design (UD) and double weighted regression (DWR) was presented. In the proposed method, the basic principle of the iteratively adaptive response surface method is applied. Uniform design is used to sample the fitting points. And a double weighted regression system considering the distances from the fitting points to the limit state surface and to the estimated design points is set to determine the coefficients of the response surface model. Compared with the conventional approaches, the fitting points selected by UD are more representative, and a better approximation in the key region is also observed with DWR. Numerical examples show that the proposed method has good convergent capability and computational accuracy.     

Dynamic reliability analysis of spacial flexible beam

In order to investigate the dynamic response reliability of the spacial flexible beam, the Monomial Cubature Rules (MCR) based Stochastic Response Surface Method (SRSM) is applied to derive the surrogate model of the nonlinear implicit limit state function. A small set of sample pairs for flexible beam dynamic response is generated by taking the integral points of MCR as sample points. Based on these sample pairs and SRSM, the surrogate model of the implicit limit state function is established. The results show that the proposed method has an excellent performance in terms of accuracy and efficiency compared with the Probabilistic Collection Method (PCM) based SRSM and Monte Carlo method, and that the dispersion of system parameters has a significant effect on the dynamic response reliability of the spacial flexible beam.     

基于序列代理模型的结构可靠性分析方法

工程中部件或系统的性能函数通常是隐函数形式,该文提出基于高效代理模型的结构可靠性分析方法,构造新增样本点学习函数,并用于指导在序列迭代过程中的样本点选择。所提出的学习函数考虑了变量权重并保证所选的样本点相互之间有一定的距离且分布在极限状态方程周围。算例分析表明该方法有较好的精度和鲁棒性,不仅适用于性能函数为隐函数时的结构可靠性分析,而且也适用于现有的各种代理模型（神经网络、支持向量机、响应面等）,为结构可靠性分析提供新途径与新方法。     

结构可靠度分析的响应面法和随机响应面法的比较

从拟合功能函数方法、计算精度与效率、收敛性等方面对响应面法和随机响应面法进行了系统地分析.算例表明:与响应面法相比,随机响应面法实现了真正意义上的非侵入式分析.响应面法采用二次多项式响应面函数仅仅在验算点附近能较好地拟合真实功能函数,而随机响应面法采用高阶Hermite随机多项式,能在整个空间上很好地拟合真实功能函数.当随机变量个数较少时,随机响应面法的计算精度和效率均优于响应面法.并且随机响应面法可进行自身的收敛性分析,确定最优阶次的计算结果作为精确解,其收敛性也优于响应面法.     

可靠性分析的改进加权响应面法

为了克服响应面法(Response surface method简称RSM)在计算大规模工程时效率低下和计算可靠性指标敏感度时偶尔误差大的问题,提出一个高效率的改进加权响应面方法.此方法首先构造一次响应面函数,然后在可能存在失效点的被缩小范围内采用轴向采样来得到样本点,构造二次响应面函数;通过从之前的样本组里增加新的样本点,给予靠近失效点的样本点更高的权重来更新响应面函数.通过几个算例表明:比较双加权响应面方法,此方法具有更高的准确性和计算效率.     

多随机变量响应面法在结构可靠性分析中的应用

基于样条函数拟合曲面响应面法,给出确定实验点和拟合响应面的方法,提出一种适用于响应面的一次二阶矩优化算法.算例表明,所提出的拟合曲面响应面算法具有使用简单和计算精度高的特点.     

Design optimization of transonic compressor stage using CFD and response surface model

In order to shorten the design period, the paper describes a new optimization strategy for computationally expensive design optimization of turbomachinery, combined with design of experiment (DOE), response surface models (RSM), genetic algorithm (GA) and a 3-D Navier-Stokes solver(Numeca Fine). Data points for response evaluations were selected by improved distributed hypercube sampling (IHS) and the 3-D Navier-Stokes analysis was carried out at these sample points. The quadratic response surface model was used to approximate the relationships between the design variables and flow parameters. To maximize the adiabatic efficiency, the genetic algorithm was applied to the response surface model to perform global optimization to achieve the optimum design of NASA Stage 35. An optimum leading edge line was found, which produced a new 3-D rotor blade combined with sweep and lean, and a new stator one with skew. It is concluded that the proposed strategy can provide a reliable method for design optimization of turbomachinery blades at reasonable computing cost.     

Structural Reliability Analysis for Implicit Performance with Legendre Orthogonal Neural Network Method

In order to evaluate the failure probability of a complicated structure, the structural responses usually need to be estimated by some numerical analysis methods such as finite element method (FEM). The response surface method (RSM) can be used to reduce the computational effort required for reliability analysis when the performance functions are implicit. However, the conventional RSM is time-consuming or cumbersome if the number of random variables is large. This paper proposes a Legendre orthogonal neural network (LONN)-based RSM to estimate the structural reliability. In this method, the relationship between the random variables and structural responses is established by a LONN model. Then the LONN model is connected to a reliability analysis method, i.e. first-order reliability methods (FORM) to calculate the failure probability of the structure. Numerical examples show that the proposed approach is applicable to structural reliability analysis, as well as the structure with implicit performance functions.     

径向基函数随机响应面法

针对随机响应面法对非正态分布响应与标准正态分布输入之间的复杂非线性隐函数拟合不够理想的问题,基于径向基函数在杂散数据拟合方面的优异性能,提出使用径向基函数替换Hermite多项式来解决复杂非线性隐函数拟合问题.以若干个非线性解析函数和钢管混凝土肋拱极限承载力不确定性问题作为算例,验证该方法对非正态分布响应拟合的精确性和对工程问题的适用性.算例结果表明,基于径向基函数随机响应面法对高度非线性的响应与输入隐函数拟合较好;在多参数钢管混凝土拱极限承载力不确定性问题中,精度较高,且比Hermite多项式样本点数量少.     

拼焊板成形过程控制参数优化设计

为解决拼焊板（TWB）成形数值模拟中的强非线性问题并消除计算噪声效应，提出了一种基于近似优化技术的最佳成形过程参数求解方法.采用响应面方法（RSM）构造每次优化迭代的目标和约束逼近曲面，逐次迭代收敛得到全局最优解.借助空间映射（SM）技术的代理模型求解响应面和相关优梯度，利用一个精细模型为下一优化迭代修正设计点.选取拉延筋成形阻力和压边力控制参数为设计变量，选取成形极限图（FLD）标准为约束条件，建立最小化焊缝偏移量为目标函数的优化模型.优化计算结果表明，该方法能有效求解拼焊板成形过程参数，使焊缝有害偏移量减少75%以上.     

Vibration reliability analysis for aeroengine compressor blade based on support vector machine response surface method

To ameliorate reliability analysis efficiency for aeroengine components, such as compressor blade, support vector machine response surface method(SRSM) is proposed. SRSM integrates the advantages of support vector machine(SVM) and traditional response surface method(RSM), and utilizes experimental samples to construct a suitable response surface function(RSF) to replace the complicated and abstract finite element model. Moreover, the randomness of material parameters, structural dimension and operating condition are considered during extracting data so that the response surface function is more agreeable to the practical model. The results indicate that based on the same experimental data, SRSM has come closer than RSM reliability to approximating Monte Carlo method(MCM); while SRSM(17.296 s) needs far less running time than MCM(10958 s) and RSM(9840 s). Therefore,under the same simulation conditions, SRSM has the largest analysis efficiency, and can be considered a feasible and valid method to analyze structural reliability.     

基于帕德逼近响应面法的边坡可靠度分析

边坡工程在进行稳定性分析评价时,通常其功能函数呈现出高度非线性隐式特性,从而导致无 法直接求解其可靠度。因此,提出将数值分析中的帕德有理逼近与可靠度分析中的响应面法相结合,利用帕 德逼近有理多项式拟合响应面函数。并采用拉丁超立方试验构造样本,将样本数据代入简化 Bishop 算法中 得到边坡功能函数值,求解得到代理模型待定系数,从而实现隐式功能函数显式化。且基于 Matlab 程序语 言编制 JC 法可靠度指标计算程序,建立了基于帕德逼近有理多项式的边坡稳定可靠度分析新方法（PRSM）。 通过两个经典的边坡算例,验证了所提方法的可行性、计算的高效性及准确性。最后,将所提方法应用于某 实际边坡工程中,计算结果表明,该边坡工程失稳的可能性较低,与实际监测结果吻合。     

结构形状优化响应面方法的改进与应用

为了克服了二维连续体形状优化过程中解析敏度求解困难的问题,利用响应面方法将目标函数和约束函数近似显式化,并建立了位移应力约束下的形状优化序列二次规划模型;为了克服响应面方法不够准确的缺点,将响应面方法进行改造,使其在设计点上取精确值;提出了改良的试验设计方法,达到了以较少的结构分析代价构造约束响应面的目的;通过建立二次评价函数,确定了具有自适应能力的运动极限,形成了具有较少计算量和较高逼近精度的优化策略.算例说明这种策略是有效而稳定的.     

轿车侧碰中车门抗撞性的快速优化

针对汽车侧面碰撞时吸收能量的重要部件——车门结构,进行了快速抗撞性优化设计。将提高车门结构吸能量作为优化目标,选择主要部件的板厚为设计变量,建立抗撞性优化问题的数学模型。基于均匀试验设计方法快速合理地分布样本点。根据多项式响应面方法构造原优化问题的高精度近似模型。采用粒子群优化算法对近似模型进行优化设计。优化结果证明了本文提出的快速抗撞性优化设计方案的可行性及有效性,对车辆被动安全分析具有较高的工程应用价值。     

表面响应算法及其在MRI主磁体优化设计中的应用

通过将基于径向基函数的表面响应模型和改进的遗传算法相结合，提出了一种电磁场逆问题优化策略的新方法；该方法一方面利用表面响应模型能够大大节省目标函数评价的时间，另一方面通过改进遗传算法能加速收敛，从而节省了寻优时间.这一方法已应用于永磁完全开放式磁共振成像仪主磁体结构的优化设计.此外，给出了一种产生薄片型磁场的永磁全开放式磁共振成像仪主磁体结构.计算实例表明，所提出的算法能实现多变量寻优，且能大大节省计算时间，易于编程实现.     

改进复合形法及其在边坡稳定分析中的应用

基本复合形法寻优考虑了复形顶点目标函数的改进,但忽略了保持复形顶点的多样性,从而有可能使算法易陷入局部极优．为此,进行了以下改进：对每个顶点构造寻优直线,即该顶点与其余顶点几何中心的连线;在该直线上寻找该顶点的改善点并替换掉该顶点构造新的复形;在构造的多个新复形中,选择多样性最强的新复形作为本次迭代产生的复形;如此迭代直至没有新的复形产生．顶点多样性采用复形相似距度量．通过对1个复杂边坡最小安全系数的搜索证明,这些改进措施是有效的．     

基于序列响应面方法的协同优化算法

分析了响应面协同优化的计算结构，指出影响计算结果准确度的因素，即计算过程中存在选择响应面样本点及响应面更新的问题，这是两个相互耦合的问题。分析了产生这个问题的原因并提出了一种将修正的置信域方法与中心组合设计相结合的序列响应面算法，系统地解决了这个问题。仿真算例表明由该算法得到的结果有很高的精度与鲁棒性，完全可以满足工程计算需要。     

硫酸盐法制浆蒸煮终点预测模型

为了实现制浆蒸煮终点的精确预测，建立了基于广义回归神经网络（GRNN）的预测模型．GRNN具有很强的非线性映射能力，能够根据样本数据逼近自变量与因变量之间隐含的关系，平滑参数的确定是GRNN训练的实质和难点．均衡地兼顾GRNN模型的预测性能与训练可行性，提出了一种平滑参数优化方法．通过分析训练样本分布、恰当地设计适应度函数，运用优进遗传算法（EGA）实现参数寻优．通过实验表明，所建立的制浆蒸煮终点预测模型，预测精度高、稳定性能好．     

Combined Size and Shape Optimization of Structures with DOE, RSM and GA

In this paper,size and shape optimization problem of a machine gun system is addressed with an efficient hybrid method,in which a novel and flexible mesh morphing technique is employed to achieve fast parameterization and modification of complexity structure without going back to CAD for reconstruction of geometric models or to finite element analysis (FEA) for remodeling.Design of experiments (DOE) and response surface method (RSM) are applied to approximate the constitutive parameters of a machine gun system based on experimental tests.Further FEA,secondary development technique and genetic algorithm (GA) are introduced to frnd all the optimal solutions in one go and the optimal design of the demonstrated machine gun system is obtained.Results of the rigid-flexible coupling dynamic analysis and exterior ballistics calculation validate the proposed methodology,which is relatively time-saving,reliable and has the potential to solve similar problems.     

响应面方法及其在食品工业中的应用

响应面方法是利用合理的试验设计并通过对实验数据进行一定的处理,建立影响因素与响应值之间的函数关系,得到一个回归方程,通过对回归方程进行分析,选择最优工艺参数.这种方法已广泛应用于粮油食品、化学化工等方面的工艺配方设计及加工工艺条件的优化.本文就响应面方法的优点、试验设计的方法以及实验数据的处理进行了简单的阐述,对其应用的限制因素进行一一说明,并就具体应用列举了一个简单的实例.